1 /* ----------------------------------------------------------------------
2 * Copyright (C) 2010-2012 ARM Limited. All rights reserved.
3 *
4 * $Date: 17. January 2013
5 * $Revision: V1.4.0
6 *
7 * Project: CMSIS DSP Library
8 * Title: arm_convolution_example_f32.c
9 *
10 * Description: Example code demonstrating Convolution of two input signals using fft.
11 *
12 * Target Processor: Cortex-M4/Cortex-M3
13 *
14 * Redistribution and use in source and binary forms, with or without
15 * modification, are permitted provided that the following conditions
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19 * - Redistributions in binary form must reproduce the above copyright
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22 * distribution.
23 * - Neither the name of ARM LIMITED nor the names of its contributors
24 * may be used to endorse or promote products derived from this
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26 *
27 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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39 * -------------------------------------------------------------------- */
40
41 /**
42 * @ingroup groupExamples
43 */
44
45 /**
46 * @defgroup ConvolutionExample Convolution Example
47 *
48 * \par Description:
49 * \par
50 * Demonstrates the convolution theorem with the use of the Complex FFT, Complex-by-Complex
51 * Multiplication, and Support Functions.
52 *
53 * \par Algorithm:
54 * \par
55 * The convolution theorem states that convolution in the time domain corresponds to
56 * multiplication in the frequency domain. Therefore, the Fourier transform of the convoution of
57 * two signals is equal to the product of their individual Fourier transforms.
58 * The Fourier transform of a signal can be evaluated efficiently using the Fast Fourier Transform (FFT).
59 * \par
60 * Two input signals, <code>a[n]</code> and <code>b[n]</code>, with lengths \c n1 and \c n2 respectively,
61 * are zero padded so that their lengths become \c N, which is greater than or equal to <code>(n1+n2-1)</code>
62 * and is a power of 4 as FFT implementation is radix-4.
63 * The convolution of <code>a[n]</code> and <code>b[n]</code> is obtained by taking the FFT of the input
64 * signals, multiplying the Fourier transforms of the two signals, and taking the inverse FFT of
65 * the multiplied result.
66 * \par
67 * This is denoted by the following equations:
68 * <pre> A[k] = FFT(a[n],N)
69 * B[k] = FFT(b[n],N)
70 * conv(a[n], b[n]) = IFFT(A[k] * B[k], N)</pre>
71 * where <code>A[k]</code> and <code>B[k]</code> are the N-point FFTs of the signals <code>a[n]</code>
72 * and <code>b[n]</code> respectively.
73 * The length of the convolved signal is <code>(n1+n2-1)</code>.
74 *
75 * \par Block Diagram:
76 * \par
77 * \image html Convolution.gif
78 *
79 * \par Variables Description:
80 * \par
81 * \li \c testInputA_f32 points to the first input sequence
82 * \li \c srcALen length of the first input sequence
83 * \li \c testInputB_f32 points to the second input sequence
84 * \li \c srcBLen length of the second input sequence
85 * \li \c outLen length of convolution output sequence, <code>(srcALen + srcBLen - 1)</code>
86 * \li \c AxB points to the output array where the product of individual FFTs of inputs is stored.
87 *
88 * \par CMSIS DSP Software Library Functions Used:
89 * \par
90 * - arm_fill_f32()
91 * - arm_copy_f32()
92 * - arm_cfft_radix4_init_f32()
93 * - arm_cfft_radix4_f32()
94 * - arm_cmplx_mult_cmplx_f32()
95 *
96 * <b> Refer </b>
97 * \link arm_convolution_example_f32.c \endlink
98 *
99 */
100
101
102 /** \example arm_convolution_example_f32.c
103 */
104
105 #include "arm_math.h"
106 #include "math_helper.h"
107
108 /* ----------------------------------------------------------------------
109 * Defines each of the tests performed
110 * ------------------------------------------------------------------- */
111 #define MAX_BLOCKSIZE 128
112 #define DELTA (0.000001f)
113 #define SNR_THRESHOLD 90
114
115 /* ----------------------------------------------------------------------
116 * Declare I/O buffers
117 * ------------------------------------------------------------------- */
118 float32_t Ak[MAX_BLOCKSIZE]; /* Input A */
119 float32_t Bk[MAX_BLOCKSIZE]; /* Input B */
120 float32_t AxB[MAX_BLOCKSIZE * 2]; /* Output */
121
122 /* ----------------------------------------------------------------------
123 * Test input data for Floating point Convolution example for 32-blockSize
124 * Generated by the MATLAB randn() function
125 * ------------------------------------------------------------------- */
126 float32_t testInputA_f32[64] =
127 {
128 -0.808920, 1.357369, 1.180861, -0.504544, 1.762637, -0.703285,
129 1.696966, 0.620571, -0.151093, -0.100235, -0.872382, -0.403579,
130 -0.860749, -0.382648, -1.052338, 0.128113, -0.646269, 1.093377,
131 -2.209198, 0.471706, 0.408901, 1.266242, 0.598252, 1.176827,
132 -0.203421, 0.213596, -0.851964, -0.466958, 0.021841, -0.698938,
133 -0.604107, 0.461778, -0.318219, 0.942520, 0.577585, 0.417619,
134 0.614665, 0.563679, -1.295073, -0.764437, 0.952194, -0.859222,
135 -0.618554, -2.268542, -1.210592, 1.655853, -2.627219, -0.994249,
136 -1.374704, 0.343799, 0.025619, 1.227481, -0.708031, 0.069355,
137 -1.845228, -1.570886, 1.010668, -1.802084, 1.630088, 1.286090,
138 -0.161050, -0.940794, 0.367961, 0.291907
139
140 };
141
142 float32_t testInputB_f32[64] =
143 {
144 0.933724, 0.046881, 1.316470, 0.438345, 0.332682, 2.094885,
145 0.512081, 0.035546, 0.050894, -2.320371, 0.168711, -1.830493,
146 -0.444834, -1.003242, -0.531494, -1.365600, -0.155420, -0.757692,
147 -0.431880, -0.380021, 0.096243, -0.695835, 0.558850, -1.648962,
148 0.020369, -0.363630, 0.887146, 0.845503, -0.252864, -0.330397,
149 1.269131, -1.109295, -1.027876, 0.135940, 0.116721, -0.293399,
150 -1.349799, 0.166078, -0.802201, 0.369367, -0.964568, -2.266011,
151 0.465178, 0.651222, -0.325426, 0.320245, -0.784178, -0.579456,
152 0.093374, 0.604778, -0.048225, 0.376297, -0.394412, 0.578182,
153 -1.218141, -1.387326, 0.692462, -0.631297, 0.153137, -0.638952,
154 0.635474, -0.970468, 1.334057, -0.111370
155 };
156
157 const float testRefOutput_f32[127] =
158 {
159 -0.818943, 1.229484, -0.533664, 1.016604, 0.341875, -1.963656,
160 5.171476, 3.478033, 7.616361, 6.648384, 0.479069, 1.792012,
161 -1.295591, -7.447818, 0.315830, -10.657445, -2.483469, -6.524236,
162 -7.380591, -3.739005, -8.388957, 0.184147, -1.554888, 3.786508,
163 -1.684421, 5.400610, -1.578126, 7.403361, 8.315999, 2.080267,
164 11.077776, 2.749673, 7.138962, 2.748762, 0.660363, 0.981552,
165 1.442275, 0.552721, -2.576892, 4.703989, 0.989156, 8.759344,
166 -0.564825, -3.994680, 0.954710, -5.014144, 6.592329, 1.599488,
167 -13.979146, -0.391891, -4.453369, -2.311242, -2.948764, 1.761415,
168 -0.138322, 10.433007, -2.309103, 4.297153, 8.535523, 3.209462,
169 8.695819, 5.569919, 2.514304, 5.582029, 2.060199, 0.642280,
170 7.024616, 1.686615, -6.481756, 1.343084, -3.526451, 1.099073,
171 -2.965764, -0.173723, -4.111484, 6.528384, -6.965658, 1.726291,
172 1.535172, 11.023435, 2.338401, -4.690188, 1.298210, 3.943885,
173 8.407885, 5.168365, 0.684131, 1.559181, 1.859998, 2.852417,
174 8.574070, -6.369078, 6.023458, 11.837963, -6.027632, 4.469678,
175 -6.799093, -2.674048, 6.250367, -6.809971, -3.459360, 9.112410,
176 -2.711621, -1.336678, 1.564249, -1.564297, -1.296760, 8.904013,
177 -3.230109, 6.878013, -7.819823, 3.369909, -1.657410, -2.007358,
178 -4.112825, 1.370685, -3.420525, -6.276605, 3.244873, -3.352638,
179 1.545372, 0.902211, 0.197489, -1.408732, 0.523390, 0.348440, 0
180 };
181
182
183 /* ----------------------------------------------------------------------
184 * Declare Global variables
185 * ------------------------------------------------------------------- */
186 uint32_t srcALen = 64; /* Length of Input A */
187 uint32_t srcBLen = 64; /* Length of Input B */
188 uint32_t outLen; /* Length of convolution output */
189 float32_t snr; /* output SNR */
190
main(void)191 int32_t main(void)
192 {
193 arm_status status; /* Status of the example */
194 arm_cfft_radix4_instance_f32 cfft_instance; /* CFFT Structure instance */
195
196 /* CFFT Structure instance pointer */
197 arm_cfft_radix4_instance_f32 *cfft_instance_ptr =
198 (arm_cfft_radix4_instance_f32*) &cfft_instance;
199
200 /* output length of convolution */
201 outLen = srcALen + srcBLen - 1;
202
203 /* Initialise the fft input buffers with all zeros */
204 arm_fill_f32(0.0, Ak, MAX_BLOCKSIZE);
205 arm_fill_f32(0.0, Bk, MAX_BLOCKSIZE);
206
207 /* Copy the input values to the fft input buffers */
208 arm_copy_f32(testInputA_f32, Ak, MAX_BLOCKSIZE/2);
209 arm_copy_f32(testInputB_f32, Bk, MAX_BLOCKSIZE/2);
210
211 /* Initialize the CFFT function to compute 64 point fft */
212 status = arm_cfft_radix4_init_f32(cfft_instance_ptr, 64, 0, 1);
213
214 /* Transform input a[n] from time domain to frequency domain A[k] */
215 arm_cfft_radix4_f32(cfft_instance_ptr, Ak);
216 /* Transform input b[n] from time domain to frequency domain B[k] */
217 arm_cfft_radix4_f32(cfft_instance_ptr, Bk);
218
219 /* Complex Multiplication of the two input buffers in frequency domain */
220 arm_cmplx_mult_cmplx_f32(Ak, Bk, AxB, MAX_BLOCKSIZE/2);
221
222 /* Initialize the CIFFT function to compute 64 point ifft */
223 status = arm_cfft_radix4_init_f32(cfft_instance_ptr, 64, 1, 1);
224
225 /* Transform the multiplication output from frequency domain to time domain,
226 that gives the convolved output */
227 arm_cfft_radix4_f32(cfft_instance_ptr, AxB);
228
229 /* SNR Calculation */
230 snr = arm_snr_f32((float32_t *)testRefOutput_f32, AxB, srcALen + srcBLen - 1);
231
232 /* Compare the SNR with threshold to test whether the
233 computed output is matched with the reference output values. */
234 if( snr > SNR_THRESHOLD)
235 {
236 status = ARM_MATH_SUCCESS;
237 }
238
239 if( status != ARM_MATH_SUCCESS)
240 {
241 while(1);
242 }
243
244 while(1); /* main function does not return */
245 }
246
247 /** \endlink */
248